Method of forming helicoidal surfaces



.June 9, 1925. f A 1,540,757

\ b, E. BUGKINGHAM.`

METHOD 'oF FoRMNpT HELICOIDAL sURFAcEs Filed March 1s'. 1922 2 seets-sn'et 1l I Junet 9, 1925-.'

l E. BUCKINGHAM Filed March 13. 192,2 2 sheets-Shana Patented .lune 9, i925.,r

lhMMSl EARLE BUCKINGHAM, OF HARTFORD, CONNECTICUT, 'ASSIGNOR/,TO IPIEtAll'l L WHIT- NEY COMPANY, OF NEW YORK, N. Y., LA CORPORATION F NEW JERSEY.

METHOD OF FORMING HELICOIDAL SURFACES. s

Application led March 13, 1922. Serial No. 543,403.

To all whom t may concern Be it known .that'L EARLn BUCKINGHAM, a citizen of the United States, residing at Hartforchin the .county4 of Hartford and State of Connecticut, have invented certain new and yuseful Improvements inMethods of Forming Helicoidal Surfaces, of which the following is a specification.

My invention relates to methods of forming involute helicoidal surfaces 'and' lparticularly to methods of forming hobs having involute helicoidal surfaces. Y 1 j One object of myinvention is to provide a simple and an eficient method of forming a.' thread having true involute helicoidal surfaces and of cuttingteeth on the thread to form-a hob. f Y i Another object of my invention is to provide a method of yforming a hob which has side relieved teethI so formed that-the effective contour behind the cutting surface of each tooth isthe same at successive surfaces of intersection similar to the initial cutting face, whereby the teeth of the hob may be ground on the front cutting faces without changing the effective contour.

Another object of my invention is to provide a method of forming a hob which has the top of each tooth radially relieved and the sides of the teeth axially relievedywhereby the effective contour behind the cutting face'cf each tooth is thesame at successive surfaces of intersection similar tothe initial cutting face. l,

Another object of my invention is to provide a method of forming hobs that shall .consist in forming a thread on a blank, in cutting` the sides of the thread to true .in-

volute helicoids, in cuttingflutes on the blank through the thread, in axially relieving the sides of the blank teeth, -in radially relieving the top' cutting edge of the teeth, and in grinding the cutting` faces and the side cutting edgesfof the teeth. A further object .of my invention is provide a method of form-ing hobs that shall `consist in milling a thread on a blank, in cutting each side of the thread with a straight cutting edge to form true involute helicoidal surfaces` each cutting edge being niaintained tangent to the base cylinder of the desired involute helicoid and at a predetermined angle to a plane perpendicular to the blank axis` in cutting flutes on the blank through the thread to form teeth, in

i tov l.axiallyY relieving the sides of 4the teeth, in radially relieving the tops of the teeth and in grinding` the cutting faces .andthe side cutting edges of the teeth.

` Hobs, which are constructed in accordance with my mvention, are particularly adapted for cutting gear wheels having. involute teeth but are' not necessarily limited to such operation. A gear wheel having involute teeth is adapted to mesh with a rack having uniform lead, vstraight cutting edges inclined at any predetermined angle'- to a plane perpendicular to the hob axis. The cutting edges remain tangent to a cylinder of a diameter that the helix angle of the helicoidal surfaces at such a diameter isthe same as the anglel between the'v generating cutting edges and the plane perpendicular to the hob axis.. An involute helicoidal surface may be considered ,thesurface which is obtained by rotating an involute while ad vancing it along the axis thereof at a uniform rate. .The involute helicoid may also be 4stated as the surface which is obtained.

by screwing an involute along its axis.

The first conception of a vhob for cutting gear Wheels-was aworm Whereinan axial section is the same as the rack which is used as the vbasis for a'n involute kgear wheel.

.Each side of such a Worm is formed by a `tool having a straight cutting edge making any predetermined angle with a plane perpendicular to the blank axlsvand extending along,a line passing through the axis of the blank. The straight cutting edge is assumed to be revolved and advanced with a uniform lead. The intersection of a surface so formed and a plane perpendicular to the blank axis would be an Archimedes vspiral andv notan involute as is required. It is customary at the presentday to form a hob by'iirst cutting a thread in the above indicatedv manner and by cutting flutes on the ting edges which are tangent to the base cylinder of the desired involute helicoid and makeA a predetermined angle With planesI perpendicular to the blank axis. One cutting edge serves to cut one sideof' the thread Whereas the other cutting edge serves' to cut the other side ofthe thread. Suchcutting .edges may, if so desired, operate simultaneously on theblank '-`Whenoperating simultaneously on a blank, the c utting edges are located in .the angular positions above set forth andl tangent to the base cylinder of the desired involute o n opposite sides of the blank axis. `If so desired, the same cutting tool may be utilized for cutting a true involute helicoidal surface 'on each side of the thread. .In such case-one I side of the blank thread` is first cut'to a true involute helicoid and then the position 4of the blank is reversed and .theA other side of the thread is cut to a true` involute helicoidv by the same .cutting tool and .the saine straight. cutting edge. 'Upon cutting the the Work.

i in

sides of the thread to true involute helicoids, suitable iutes are cut on the blankt-hrough the thread'.` Such flutes may be straight or spiralas desired'. The inclination of, the spiral flutesivr'x'nay be in either, direction,as desired, according to the character of Work being operated on.;V Moreover, the cutting faces ofthe teeth, Which-are formed by the flutes, vmay be radially `ornon-radially arranged, as desired. j`

It is customary to provide straight flutes in order to give a more even cutting action. IIoweiler` straight flutes will not givesuch a smooth cutting'action if the hob 4is set square With the Work or the generating rack,

`as Will be pointed out) hereinafter. The hob may --be set at any desired angle relative to The flutes should be formed on the hob in accordance With thehelix angle or lead on thehob. If the helix angle of the 'hob is relatively large, the use of straight flutes will result in a'. blunt cutting edge on one vside of eachA hob tooth and aiaelatively acute angle on the other side of each tooth. In such case it is necessary tousehehcal cut`r` ting fluteswhich will be substantially .per-

to maintain suitable cutting edges. f

Upon forming-of teethon the 'hob by cutting flutes through the thread, the side cutting edges oftheteeth. are axlallyrelieved and the/top cutting edges are radially re` lieved. The axial relief on the teeth is preferably effected by means o.f a formed lathe tool which is matched to the form of the teeth at the sidecutting edges formed by the hob liutes. Each side. of the teeth is relieved by such a relieving tool in thel usual .and customary manner.' Upon completion -of the axial relief on the hob teeth, the tops of the teeth are radially relieved in. the

'customaryand usual manner. The tops of' 'the hob teeth must be radially relieved to 7, such an extent that the thickness of the teeth the inclination ofthe flutes and preferably the side` cutting .edges are so ground asto make very little or slight drag. It, of

course, will be preferableto grind the side relieved surfacesibut such operation is somewhat-expensive and a slight grinding of the side cutting edges produces satisfactory results. i

lIt has been determined that the contact surface of gear Wheels, which have been cut pitch line. lIn referring to a usual or ordi nary hob, a heb is considered which is formed by a straight cutting edge making a predetermined angle with a plane perpendicular .to'theblank axis and extending along a lineV passing through the blank axis. The

' retically almostjall of the involute profile in involute'gear teeth should bein the con-v 'tact-ing surface.' 'Accordingly due to `the -narrow bearing face 'on involute gears, as

although the thickness at the pitch line may be correct. The hob, which is generated in accordance -With my method does not have- .now constructed by the hobbin'g process',the

a straight line profile at the cutting edge'as the hob which is generated in accordance with the common and usual method. It has been determined. however, thatthe larger the diameter of the hob, the more nearlythe hob tooth profile approaches a straight line.

It would seem advisable'to make' the diameteipof the hob as large as conditions will permit. However, a large hob not only costs is even more diicult to grind.

more butthe lead of larger d-iametered hobs is distorted more in hardening than the lead of smaller diametered hobs.

lVhen a hob has been formed by a radially arranged cutting edge, as by the methods above set forth, it is ditlicult to grind and maintain the surfaces of the sides of the hob teeth. It is well known that it is not possible to grin-d a continuous screw thread with any degree of accuracy unless the-lead of the thread is very small. The reason for the difficulty in grinding screw threads is the inability of the grinding wheel to cutl along the same cutting line by which' the thread is formed. If it difficult to grind a continuous screw thread, itA is apparent that a relieved screw thread, which is attempted on the sides of the hob teeth, Therefore, in grinding screw thread hobs, it is apparentv two errors are introduced, the error of the screw thread and the erroretfected in attempting to grind screw threads.

In a hobiconstructed in accordance with ,my methods, the sides ofthe hob teeth are axially relieved to an abnormal extent for a purpose to be hereinafter set forth. Such side relieved surfaces are-inthe form ofinvolute helicoids. Althougha hob may be formed with teeth which will cut substantially correct involute teeth, errors are' introduced during thehardening process which distort'the hob teeth. have been formed by a radially arranged cutting edge as heretofore set forth, -it is a very ditlicult matter tov so grind the hob as to eliminate the errors introduced during hardening. `In a heb having .teeth the side surfaces of which are in the form of true involute helicoids, the correcting of the hardening errors is greatly simplified. Although the sides of the hob teeth may be correctly ground inasmuch as they are in the form of involute helicoids, it has been found that -the contour grinding of the side edges of the'teeth will give very satisfactory results. The side cutting edges are ground to true' involute helicoids having the same lead as the lead'of the hob thread. Inasmuch as the sides of the teethhave been axially relieved, to an appreciable extent, it

is apparent the contour grinding/'vill gri-nd onlyta very narrow ribbon on the sides of the teeth. Such ribbon will be so narrow as not to produce any appreciable. lag or drag. The front cutting faces of the teeth should be ground in the usual 'manner in conformity 'with the direction of the flutes and in conformity with the front cuttingfaces ofthe'teeth. The front cutting faces" of the teeth may be ground a number of times ``without cont-our grinding the side' cutting ec ges of the teeth.-`

' {nfmy companion application, Serial No. 543,404 tiled March 13, 1922, is disclosed and In hobs which claimed, hobs which are constructed in acapplication.

lin the accompanying drawings: v

.Figure 1 is a diagrammatic view showing the intersections of various planes with a rack having straight sided teeth. 1

Fig. 2 is a view similar to Fig. 1 showing the lines of contact between the teeth of a hob with thc straight sided teeth of a rack.

Fig. 3 is a diagrammatic view coniparing` radial and axial relief on a tooth of a hob having true i-nvolute helicoidal surfaces.`

Figs. 4f andj 5 are diagrammatic views7 showing the positions of al formed lathe tool for axially relieving hobs having teeth provided with non-radially arranged .cutting lfaces and teeth provided with 'radially rc- .lieved cutting faces.

Fig. 6 is a diagrammatic view more clearly showing the lines of contact between the teeth of the hob -and the teeth of the rack shown in Fig. 2.' Y

.Fig. 7 is a diagrammatic end view of a Ahob andthe position of the cutting edges forforming true involutc helicoidal surfaces.

Fig. 8 is a partial side elevational view of the hob and cutting edges shown in Fig. 7.

Fig. 9v is-a partial plan vieu' of the hoh and tools shown in Fig. 7.

in accordance with my invention.

Fig. 12 1s a diagrammatic view illustrating the lead of the hob at the pitch circle.y

In referring to the drawings, a hob will be considered which will4 generate a rack having straight sided teeth. Although such a., rack would never be constructed by a hob, it is simpler to consider a hob in connection with a rack Rather than in connection kwith a. lgear wheel having involrtfi teeth. It is well known that a raclrhaviug straight sided teeth 'is used'as a base for a gear wheel havingl 'involute teeth. vMoreover, a hob, which willcut involute teethi;l

on a g'ear wheel, will also cut straight sid-cd teeth on a rack. Although ahob consists of teeth formed in a continuous thread or threads',rit is simpler to consider the continuous thread of a-hob wit-hout regard to the teeth which are cut therein.. Accordingly in referring to Figs. l, 2 and G of the drawings, a worm or a heb without teeth formed in the thread will be considered as meshing with a rack having straight 'side-l teeth. It is to be understood that the hob thus considered, may have teeth of any desired shape or form which will me'slrwith the teeth of a rack in the same manner as a worm thread. i

Referring to Fig. l. of the drawings, three views of a rack 1 are illustrated. The rack of a worin or hob which meshes with'the teeth on the ra-ck. The axis 0 makes an angle 'with the line .b--ZL The line b-b drawn in the plane of the teeth and perf pendicularly to them. It also may be stated,

the axis c-cinakes an angle with a verti cal plane through the rack. The vertical plane is drawn perpendiculai'ly to the di,-4 rection ot' the rack teeth. The sides. 3 of the rack teeth .are `considered to `make' an4- angle a with a plane perpendicular to thev rack and parallel to the direction'of the teeth, as shown in Fig. 1 of the drawings.

In each of Figs. 1, 2 and 6, three views of the basic rack have been shownl in order to inorefclearlyset ,florth the lines of engagement betweenthe sides of a hob thread and the sides of a rack having* straight sided teeth. The projection` lines in each ligure have been extended to Iioin the views in order to more clearly explain the angular setting ot the lines of engagement. The parts or portions of the Figs. 2 and 6 have been designated i`n the same manner as the parts of Fig. 1. The parts of Fig. 2 are marked 2a. 2 42C- and 2d andthe arts of Fie. 6 are marked 6, 6", 6c and 69. y

The line ya in portion laFig. 1 of the drawings represents the intersection of a plane along the line (z-a with one side 8 of a tooth2 ot' the rack. The pitch line of the rack in thepart ln of Fig. 1 of the drawings is indicated b .the reference charac-tersl The. lineot action 'between the teeth P--P.' on a 4hob (not shown in'Fig. 1 of the drawings) must be along aline perpendicular to the line y2'. 'Moreover, the line `of action must pass through the pitch line P- P and must also intersect the center line or axis c-c of the hob. part ln of Fig. 1 must pass through the in-y tersection point between the line P-P and the axis c`-c and must also be perpendicular to the line 1/2. The portion no of the line cZ-d, as shown in part 1a of Fig. 1, is a line along which a side oi a hob thread having an'axis c-c must engage thc side of a rack tooth. In brief, the portion hoof-the line d-tZ is the line ot engagement between the side of a rack tooth and the side of a worin thread.

Referring to Fig. 2 of the drawings, a worm or hob 10 is shown meshing with the l rack l. l The worm l0 isset at an angle tl Therefore, the line cil-ai in with respect to the rack 1. The wormis provided with a thread 11 having sides 12 which correct-ly engage the straight sides of worin thread so engages the sides of the rack teeth as to cut straight sided teeth if the worm is kused as a hob. -As heretofore set forth, the views of the rack in Fig. 2 are assumed to be similar to the views vof the' rack shown in Fig. 1 of the drawings.

` The line d-d makes an angle oc with a horizontal plane through'the rack in vportion la, Fig. lfof the drawings. Inasmuch asthe center line c-#o of the hob is perpendicular to the pitch line and as the linea/2 is perpendicular to the line d-t, the line ya continued 'makes an angle a with Athe center linev c -c.`f' The projection of the line of engagernent no bet-Ween the hob thread and the side of the .rack tooth from part 21 to part 2c of Fig.` 2 is shown on the side of a rack tooth inportion 2c of Fig. 2. The J line of engagement between the rack and one side of the hob thread-in part 2b of Fig. 2 is indicated by one side fg of a rack tooth. In order to show the angle which the line .of engagement makes with a plane perpendicular to the axis c-c of the hob, a section is taken along the line d-d in part 2ZL of Fig. 2. The section so 'taken is part 2dl of Fig. 2. The angle made by the line of engagement -is indicated by the reference character in part 2d of Fig. 2.;

Referring to- Fig. 2 of the drawings, it is apparent thepitch circle of the hob must engage'the pitch line P-P of the rack atthe point of intersection between the pitch line P -P. and theline 0 0. The radius of the pitch circle is taken equal to R. In

Figs. l and 2 of the drawings, only one line of engagement between .the hob thread and the straight sided tooth ,of the rack has been considered. However, it is apparent that any othersection taken parallel to the section along the line lf-a ata' different posi tion along the axis 0'c of the hob will show a simil'ai1 line no of engagement between the side of the hob thread and the side of a rack tooth. i

The line yof engagement i between the straight sided tooth of a rack and the sidel of a thread onra worm must be a 'straight lineii1 all partsof the side of the tooth. are engaged by thethi'ead of. theworm at some, time during its movement. Moreover, it.

' may be stated that if a straight cutting edge 'the cutting of the thread on the blank, the

blank is assumed to rotate Iat a uniform rate and the cutting edge is assumed to" be moved axially alongfthe blank in timed relation to the rotation thereof.

Referring to Figs. 1 and 2 and particularly to part 1aL and 2a in such figures, it' will be noted the line 1l-ai always makes an angle awith a horizontal plane. There fore, theV line d-a is alwaystangent to a base cylinder of a radius r, as shown in part Qa, Fig. E2 of thejdrawings. From the above statenients, it is apparent the side surface ot' the thread on a worm', which correetly meshes with the straight sided teeth of a rack, must be involute helicoidal sur#- faces. An involute helicoidal surface may be considered as the .surface which is gen-- l over, it may be stated that the side surface cylinder of a predetermined diameter.

of a hob, which will generate a rack having.

straight sided teeth or` a gear wheel having involute teeth, is generated by revolving and advancing, with -a uniform lead, a straight cutting edge inclined at any given angle to a..`plane perpendicular to the blank axis. The cutting" edge must remain tangent to a will be hereinafter sety forth and shown, the

diameter of the base'cylinder is such-that the helix angle of the hob thread at that diameter is the same as the angle between the generating line or cutting edge and-a plane perpendicular to thehob axis.

When a section of an involute helicoid is taken perl'iendicular to the axis thereof, an

involute will always be obtained. The involute curve thus obtained is shown in part 2 of Fig. .2. 1f a like section were taken on a screw thread hob, which has been inade in the customary manner, an Archimedes spiral would be shown in place of an involute. For a further explanation ofthe properties of an inyolute helicoid, reference may be made to the pending application of IIrnest 4VVildhaber,'.Serial No. 543,385,

' filed -arch 13, 1922, and also to my book Involute Spur Gears published in 1922 by the Niles-Bement-Pond Company.

Giganti/lute helicoid,

Referring particularly to Fig.' 6 of the drawings, thel position of the line of engagement between a hob and a rack will be determined in values of known terms. In

Fig. 6 the line of engagement has been' 1, 2 and 6 lhas vbeen, shown inV heavy lines,

the terms used in determining' the position ofthe/Cline of engagement and the value of therangle areas follows:

rzradius lof the'base cylinderof an in- Moretzradius of the pitch circle of worm or ho ca angleof the straight side of the tooth of the generating rack zangle which the worm or hob makes with the rack; y

zhelix angle-'of the hob at the radiusR; oizpressure angle of. the involute in'parts 1a, 2a and o of Figs. 1,12 and 6. (The angle oa is the projected angle of oa in parts' 1, 2 and 6, Figs. l, 2 and 6) 4lPzcireular pitch of rack; Kzlead of the hob. l

In portion 6 ofFig. 6, a triangle fgh may be formed on the line of engagement between the -hob thread and the rack. The line lies in the plane of one side of a rack tooth. The angle fghiis equal to oi, as heretofore set forth. The' side gli, which is equal to the height of one of the rack teeth, is taken equal to 1.

Therefore, fbztan ou.

In the portion 6c of the drawings,- a triangle jkl may be formed on the line of engagement. The line 77o is considered to be drawn vperpendicularly to the axis 0.-0 of the hob, as shown in Fig. 2 ofthe drawings. The base Z/c of the triangle jkl is drawn parallelly to the axis @#0 of thevhob and perpendicularlyto the line jk. The base line Z/v of the triangle jkl is divided by aline jaa The line jm is so drawn that the angle 'fjm is equal to the angle The line jm may be considered a continuation of the line Q71. which forms a. part of the triangle 4f/z. l The line ZZ: may be considered as com- In the ort-ions 62L of Fig. 6,y a triangle ynop' may e formedon the line of engage` ment. `The line pa is vdrawn parallelly to the axis c-c ofthe hob andthe line ap is drawnv perpendicularly to the line p0. It

' is apparent the angle pao formed between the line on and 7m is` equal to the angle oe.

More-over, it is apparent the line p0 is equal to numeralLthe depth of` a rack tooth.

Solving the above triangle (hop, it is clear,

np=tan a' and The triangle jhm', which is a part of the triangle jkl in Fig. 6 of the drawings, may be solved to Obtain. the length of the line mk.

Angle klm-: angle '(5. tained, in the-equation for the line Zic alomr F 1 set forth, We obtain z" v -tan a tan The length of the line ZI: may be obtained by Solving the triangle Zmg in Fig. 6 of the A triangle ow may be formed on theline drawings. The side mg of the triangle -is O f engagement in portion 6 of Fig. 6. The drawn as a continuation of the line and line vw is taken parallel to the line f the line lg is drawn perpenclieularlygto the H1 Portlon 6-1 of ig. 6 and the 'line tw S 8D line mg. The angle formed by the line 'ml drawn perpendioul'arly to the line ow. Theand the line', QZ i5 equal t0 the angle {5 angle m0 is designated by the sign 'The angle is the angle between the line of en i ZQIfhItn f gagement and a plane perpendicular to the Solving the triangle Img, blank or hob axisa tan a l Referring to the former equations, it was COS lg shown, l Therefore,l i M tana ow=no= Sln g oos and a 90' The` line Zic of the triangle le-Z is equal to wt=ilk in t ia le 7d :tanz @Sinni the l'ine Zm-i-the line r ng 7 cos tan a :BQ-0; Therefore Therefore,

11er-zwaai@ x m 95 eos tana tan ?:yt: eostana By solving the above equation, it may. be -Uw 1 shown that-f f i sin a i -uzkgtwwnz 15H12 (tanfaJfsinz sin a 1 00 GOS um. a eos tan a Referring tothe tran'glesyz'a *amista: shown in portions 1% and 11", Fig. 1 of the In solving triangles fz/aand stm, Fig. 1, '40- tlrawings, it will be shown that' 1t 1 sshoWn- 13o tana v tan ,-=t ana tan o/ Sina sin In the triangle' stx' the line t is drawn per-v md l sin a, tan a pendionlarly tothe linesx and the line'st is drawn perpendicularly to the axis; o- 'Cosa Sm -I'LJ of the' hob Inthe tmangle Wu the. angle In the trianglea b e', portion 6a of F im ,f1/2u is equal to the angle The side zu 6 .it is 'apparent t ofthe triangle yeu is equalto the height of the rack tooth Whielr'has been taken; eqal GS Oy; l, to themuneral 1.. R il" Consequently, 'lherefore,

i R Sin .'yu=st (in triangle str), i 15V.) Substltutlng thevalue of sin oa 111 the mt =fh (1n trlanglefgh 111g. 6) :tan q, above equation, and G" tana i t tan 8:. Msm2m Sm a Sm st-tana" OSF a a 1:5

Therefore, i i Manzalsmgm 71 m1 a: tana eostana R S1116 a sln' 1l (tan2 owl-S1112 Siibstituting the value of tan oa', thus ob R SD COS P Q However,

` tan oz tan a =S.

sin2 tanzte', Substituting 'the' above equation,

tan

ln F ig. l2 a triangle'is shown formed with one side equal to the lead K, and anotherside .equal to QWR, the circumference of the hob at the pitch circle. The angle of'such triangle opposite the side K must be equal to Accordingly,

' K tan Substituting in the above equation,

Substituting in the above equation,

TK (tanza -1- l) TIC However, it is apparent from the triangle f l.' g l* v cos a -R and rr-R cos a Substituting in the above equation ,TK K

Froin the above equationthe value of the angle isdetermined for setting the cutting edge to cut a true involute helicoid on the side of a hob thread. Itshould be noted that the tangent of the angle is given in terms of the lead and of the radius` of. the base'cylinder for the involute helicoid. The angle as heretofore set forth, 1s the angl-e between the cutting edge vand a plane perpendicular to thehob or blank "must be involute helicoidal surfaces.

hob, which is set square with. the face ofa I 10 and 1l of the drawings.

. sides 17.

axis. lAttentioi'i is calledl to the fact that the tangent of the helix angle of a hob at radius v' is equal to '.Therefore, the surface of a hob, which will generate a straight sided rack or a gear wheel having involute teeth, is generated by revolving and advancing with a uniform lcada stra-ight line inclined at any tangent angle with a plane perpendicular to the axis, this line remaining tangent to a cylinder of such `work may be varied at will Within certain practical limits. Reference mayy be made to my. book Involute Spur Gears, above referred to, for a further description as to the effect of varying the value of the angle It may beynoted that if so desired, the angle may be taken equal to zero. ln Diu h latter case, the hob .is set squarewith the work being operated on.

Regardless of the angular setting of the hob, the same general characteristics of the profile remain identical. yIn other words,

the profiles ofthe cutting edges of the boli spur gear blank, is identical in all essentials with a hob which is set at an angle with respect to the blank. The-only difference in the two hobs is the change in the pressure j angle pitch `and thickness of space between the teeth.

Referring to Figs. 3, 4, 5, 7, 8 and 9 of the drawings, method will be described for forming a hob such as shown in Figs.

and 9, va hob blank 15 is shown adapted to rotate on .any axis D-D. The blank is shownprovided with av thread 16 having The thread lo may be formed on the blank-in'any suitable manner' and preferably is formed either by a lathe tool having a radialcutting edge or by a formed milling cutter.- 'Ay threadso formed does not have true involute helicoidal sides but .no In Figs. 7, 8

has sides which approximate involute helif coids.- Two cutting tools 18 and 19 are shown in position for engaging opposite sidesvof the thread 16 on the hob blank 15.

The cutting tool 18 is shown positioned a distance r above the axis of the blank and the cuttingftool 19 is positioned a distance r below the axis of the blank. Thereference Lft the thread 16. It is not essential to eut the character i* is assumed to be the radius of the base cylinder f'or'the desired involute lielicoids. lVhen the cuttingl tools 18 and 10 are so positioned, it is evident, as shown in Fig. T of the drawings, that the cutting edges are tangent to a. base cylinder having a radius f'. No means is shown in the drawings for supporting and vfor effecting ro-l tation of the blank or for supporting the. cutting tools 18 and 1i). It is assumed that. any suitable machine may be provided for practicing my methods. The showing of a suitable machine for performing .the methods would needlessly complicate the drawings and is not deemed to benecessary. As shown in Fig. 9 of the drawings, the cut" ting edge of each of the tools 18 and 19 is set to make a predeterminediangle with a. plane perpendicular Ato the blank axis. The necessity for setting the cutting edges at such angle has been described heretofore. If the blank 15 is rotated at a uniform rate and the cutting tools 18 and. 19`

are moved axially -along the blank in timed relation to the blank rotation, true involute helicoidal sides `will be cut onthe thread 16.

Upon completion of the involutehelicoids on the sides ofthe thread 16, suitable flutes,

such as the straight flutes 2O shown in Figs.

10 and 11 of the drawings, are eut through flutes through the thread after forming of -the linvolute helicoids on thesides of the teeth. The flutesmay be formed on the blank prior to the yforming of the thread 16. if so desired: The Figs. 10 and 11 of the drawings show 4a completed hob 21 and willbe 'utilized in describing the steps necessary in forming a hob. The flutes 20,shown in Figs. l0 and 11 are parallel to the. axisl of the hob 2l, but if so desired, spiral flutes which are inclined in either direction' may be cut through the thread for forming teeth 22. The teeth 22 thus formed inthe thread are provided with unrelieved sides which are in the forni of trueinvolute helicoids.

lt may be noted that the tintes, which are cut through the` blank thread, may form either radially arranged or non-radially arranged cutting faces .o n the teeth. In Fig. ll of the drawings, the teeth 22 are shown provided with non-radially arrangedcutf ting faces 23; In Fig. 5' of the drawings,

a liob 24 is shown .provided with-teeth 25.

ing` gensidered, it is essential to relieve the axial relief, it is necessary to lengthen the sides of the teeth by the :so-called axial-relief 1n order to obtain the saine effect-ive contour behindthe cutting surface of each 'tooth at successive surfaces of intersection similar to the initial cutting f ace,'whereby the teethon the hob may be ground on the front cutting faces without changing their effective contour.

' 'Referring to Fig. 3 of the drawings, a tooth 3() is shown having sides 31 and atop 32. The dot and'dash lines indicate the 7 rear side edges of the. tooth if .the sides 31 are relieved by the sci-called radial relief and the dot and dash lines -il indicate the rear side edges of the toothA it' the sides' 81` are relieved bythe so-called axial relief. Although a. hob havingthe sides of the teeth relieved b V the so-called radial relief will cutua correct profile when the hob is new', it is apparentl thatan incorrect profile will be cut when the hob is reground If the sides of the -teeth are relieved by theso- `called axial relief, the tops of the teeth may be so relieved by the so-,ealled radiahrelief as to maintain the width of the tops of the teeth substantially7 constant. .In suolicase the teeth may be ground on their front cut- 'ting`fa`ces without changing the effective contour cut by them. If thesides of the hob teeth are provided with the so-called teeth somewhat in order`to l'preventintci ference withfthe bottom of the flute when 1 the teeth are ground back some-what.

Preferably, ifa ho-b is construetedin'accordance with my methods, the sides of the teeth are axially relieved. lThe correct profiles `of the relieved surfaces depend upon the character of the fluteswhich are formed on the blank. .As here fore\ stated, the fiutes may be straight e' 'spiral and may form either radially arranged `er non-radially arranged 'cut-ting faces on the teeth.

shown in Aposition for relieving one side of a tooth 25 of the lieb blank24. The cutting edge of the tool is aligned vith the fronta cutting face 26 of one ofthe teeth 2l and is groundto match the side cutting edge of,

such tooth. lVith the cutting tool lin-such position, the teeth are relieved in the customary and usual manner. It will be'noted the cuttingedge is radially arranged with respect to the blank axis. lf the teeth of the hob are provided with non-radially arranged cutting faces, the position' of the relieving tool must be changed. fReferring to Fig. 4 of the drawings, a cutting tool 36 is i shown in position for relieving the teeth 28 on the hob` blank 27.' The cutting edge of the tool 36 `is placed above the axis of the heb 27 so that such edge is parallel to the frontjcutting face of one of the teeth 28. The cutting` edge of rthe tool 36 is matched lOO -Referring to Fig. 5, a cutting tool 35 is llO to one cutting edge ofthe tooth on the hob blank. One side of each tooth is then relieved by relieving movements which are effected in vthe usual and customary manner. The inclination of the flutes relative to the blank axis is taken care of by matching the relieving tool to the cutting edges of the hob teeth. Upon relieving one side of thehob similar n'ianner.

The'tops of the hob teeth are radially relieved in the customary and usual manner.

Preferably, the to'p's of the teeth are so relieved as to maintain the width of the top ening'. It. is possible to grindthe sides' of i the teeth, which are in the form of involute helicoids, but such an operation is somewhat expensive. However, it has been found that after grinding the front cutting faces of the teeth. the side cutting edges of the teeth may be slightly -contour ground Withoutl producing' any appreciable drag. Inas'much as the teeth are axially relieved to more tha-n a normal amount, `it is apparent. the contour grinding' of the side cutting' edges Will only produce a narrow ribbon of ground surface on the sides ofthe teeth. The ribbon of ground surface is generally about one thirty-second of`an inch in Width. Such eontour grinding may `be effect-ed by placing plane grinding' Wheels 38 and 39 in the position shown in Fig. 10 of the drawings. The grinding wheels 38 and 39 are respectively provided with grinding surfaces 40 and 41'. The grinding surfaces-40 and 41 hear the same relation to the sides ofthe hob teeth as the sides of. the rack 1 in 2 bear to the Vsides '.12 of the thread 11 on the hoh 10. Thev narrow ribbons of ground surface 42. which are formed fon 'the teeth '21 of the hob shown in Figs. 10 and 1l ofthe 4drawings. willV have awlead corresponding to the lead of the hob thread and not a lead corresponding to either of the relieved` sides 4ofthe hob teeth. For a. further description -cylinder of the desired involute helicoid.

The method Iof ,forming involute helicoidal surfaces, which consists in rotating a blank, andv 1n moving straight-cutting edges along. the blank in timed relation to the' blank rotation toform a thread-having involute hehcoidal surfaces, each of said cutting edges being placed to make a predeter- A mined angle with' a plane perpendicularto the blank axis and tangent to the base cylinder of the desired involute helicoid, said pre determined angle being dependent on the lead and the radius of the base cylinder of the desired involute' helicoid.V

3. The method of forming involute hel-icoidal surfaces, which consists in rotatingia blank, in forming an involute helicoidal surface by moving a straight cutting edge along the blank, said straight cutting edge being` maintained tangent to the base cylinder of the d esired involute helicoid and at a predetern'nned angle With a plane perpendicular tothe axis of the blank and said predeter' mined angle being dependent on the lead and the radius of the .base cylinderofthe desired mvolute hehcoid, and in cuttigfa'l second involute helicoidal surface in a similar manner to form a thread having' involute helicoidal sides,

4.' The method of forming involute helicoidal surfaces,V which consists vin rotating a blank, in providing a tool having one'- straight cutting edge which is tangent to the," I

` b'ase cylinder of the desired .involute helicoid and makes a .predetermined angle with -a plane perpendicular to the axisof the blank,

said predetermined angle being dependent on the lead and the radius ofthe base cylin-l der of thedesired involute helieoid, in Inoving the tool alongtheblank to form an in'- volute helicoidal surface, in. reversing the position of the rotatingblank, and in movf i lng the tool along the rotating blank for cutting a second involute helicoidal surface. 5. The method of forming involute helicoidal surfaces, which consists 'in rotating a. blank, in providing a vtool having one straight cutting edge -Whiehis tangent to the base-cylinderof; the desired ,involute helicoid and makes a; predetermined angle With a plane perpendicular tothe axis of the blank; said predeterminedangle being dependent upon the lead and radius of the base 'involute helicoidal surface, in'revers'ing the position of the rotating blank, and in again moving the tool along the blank in timed re- `cylinder of the desired-involute helicoid, in

6. The method of forming involute heli-- coidal surfaces, which consists in rotating a blank, in axially feeding a milling cutter along the rotating blank to form a thread having approximate involute helicoidal surfaces, and in forming involute helicoidal surfaces on said thread by subjecting each consists 1n cutting a blank to foi-in a thread side of the thread to a straight cutting edge which is maintained tangent to` the base cylinder of the desired involute helicoid andA makes a predetermined angle with a plane.

perpendicular to theI axis of the blank While being moved along the blank.

7 The method of' forming involute lieli.-

coidal surfaces, Which consists in rotating a- 'blank,'in axially feeding a milling cutter along the rotating blank lto form a thread.

having approximate involute helicoidal surfaces, and in forminginvolute helicoidal surfaces on said thread by subjecting each side of the thread to a straight cutting edge which is maintained tangent to the basecylinder of the desired involute lielicoid and makes a predetermined angle with a plane perpendicular to the axis of theblank While being moved along the blank, said predetermined angle being dependentlon the lead and the radius of the base cylinder of the desired involute helicoi'd.

8. The method offorming ing involute helicoidal surfaces, which consists in rotating a blank, in providing a cutting tool having a straight cutting edge which makes apredetermined angle with av plane perpendicular to the blank axis and is tangentto the base cylinderof a desired-involute helicoid, in moving said .to'ol along the blank in timed relation to4 the blank rotation to cut an involute helicoidal surface,

in providing a second tool having a straight cutting edge which makes the samepredetermined angle With a plane perpendicular to the blank axis and is tangent to the base cylinder of the desired involute helicoid, the

two straight cutting edgesbeing tangent to the basescylinder on opposite sides' of the blank axis, and in moving'the second tool along the blank inA the saine timed relation as the first tool, p

9. The method of forming a hob, which consists in rotating a blank, in forming a thread ,on the blank having helicoidal surfaces, in cutting flutesV on the blank through the thread, and in side relieving the helicoidal surfaces on the sides of the teethvby a constant relief While maintaining the lead unchanged, whereby.; the effective contour behind each cutting surface is the same at successive surfaces of intersection similar to the initial-cuttingface.' l

10.' .The method 0f 'forming a hob, which consists'in rotating apblank, in forming a a thread hav-` havinginvolute helicoidal surfaces, in cutting flutes on the blank through the thread, in side relievingthe involute helicoidal surfacesl on the sides of the teeth, whereby the e'ective contour behind each cutting surface is the saine at successive surfaces of intersection similar to the. initial cutting face,

and in grinding the front cutting faces and the side cutting edges of the teeth.

12. The method of forming a hob, which consists in rotating a blank, in forming a thread having helicoidal surfaces, in cutting flutes on the blank lthrough the thread, in side relieving the sidesy of the teeth,` by a constant relief` ,vvhile maintaining the lcad unchanged, andy in radially relieving the tops ofthe teeth so that the effective contour behind each cutting surface is the 4'saine at successive surfaces of intersection similar to the initial cutting face.

' 18. The method of forming a hob, which consists in rotating ablank, in cutting a blank to.v form athread having involute heliu n 1 a forming a thread having involute helicoidalsides by moving straight cutting edges alon the blank in timed relation to the blan rotation, each of said cutting edges being tangent'to the base cylinder ofv the desired involute helicoid and making arpredetermined 'angle With a plane perpendicu-` lar to the blank axis, in cutting flutes on a y b lank to form teeth, in side relieving the sides of the teethand in radially relieving the tops of the'teeth.,

.the flutes and one ofthe helicoidal surfaces,

in so setting the cutting tool relative to the blank teeth that the 4cutting edge of the tool matches the cutting edge on one side of each blank tooth, in feeding the cutting tool blank to form a thread having-involute helicoidal surfaces, in cutting flutes on the blank through the. thread, in providing a formed cutting tool having a cutting edge shaped to the edge formed by the flutes and one ofv the involute helicoidal surfaces, in 'so setting the cutting tool relative to theM blank -teeth that the cutting edge on the tool matches the cutting edge on one side of each lblanlfooth, in feeding the tool alonggethe blank in accordance With vthe-*lead of the thread While effecting relieving movements,

and in relieving the opposite side of each tooth in a similar manner;

17. The method of forming a hob, which consists in rotating a blank, in cutting the blank to form a thread having involute helicoidal surfaces,' in cutting flutes on the blank through the thread. in providing a formed cutting tool having a cutting edge shaped to the edge formed by the flutes and one of the helicoidal surfaces, in so setting the cutting tool relative to the blank teeth that the cutting edge 0n the tool matches the cutting' edge on one side of the blank teeth, and in feeding theft-oel alengthe blank in accordance with the pitch ofthe blank While effecting relieving. movements,A

in relieving the oppositelside of eachtooth in a similar manner, and in'giinding the front cutting faces andl thesidecutting edges of the teeth.

18. The method of forminga hob, Willich,v

consists inrotating a blank, in forming a thread on a blank vhaving` helico-idalv `si1r faces, in cutting straight. flutes on the blank through the thread to form teeth having non-radially arranged cutting faces, in proriding a formed cutting tool having a 'cut-l ting edge shaped to the edge formed'lby the flutes on one of thehelicoidal surfaces, in so setting the cutting tool relative to the blank teeth that thecutting edgeofthe tool` matches the cutting edge on one side of eachv blank tooth, in feeding the tool along the blank in accordance with the pitch4 of the thread While effecting relieving movements, and in relieving the opposite side of cach tooth in a similar manner.

19;'T he method of forming a hob, which. consist-s in rotating a blank, in cutting the blank to form a thread on the blank having involute helicoidal surfaces, 1in cutting straight flutes on the Yblank through the thread to form teeth'having non-radially-ar ranged cutting faces, in providing a formed cutting tool having a cutting edge shaped to the edge formed by the flutes on one or the involute helicoidal surfaces, in so setting the cutting tool relative to the blank teeth that the cutting edgev of the tool matches the cutting edge onA one side of each blank tooth, in feeding the tool along-the blank in accordance with the pitch of the thread While effecting relieving movements, and in relieving the'opposite side of each tooth in a similar manner.,

20. rlhe method of forming ahob, Which consistsin rotating ablank, in cutting the blank to form a thread having invol-ute helicoidal surfaces, in cutting flutes on the blank through the thread, in providing a formed cutting tool having a cutting edge .shaped to the edge .formed by the flutes and one ofA tooth in asimilar manner.

21. The method v(if-forming a'hob, which consists in rotating a blank, in forming a thread having helico-idat surfaces, in cutting straight flutes on the blank through the thread toform teeth having non-radially arranged cutting faces, in providing a ffformed cutting tool 4having a cutting` edge shaped to the edge formed by the fluteson one of the'helicoidal surfaces', in sosetting the cutting toolrelative to the blank teeth that thel cutting edge of .the tool matches the` cutting edge on one side of each blank `,tooth, in feeding thetool along the blank in accordance With the pitch of the thread While effecting side relieving movements,l and in relieving the oppositeside of each tooth in a similarmanner. l

22, The method of forming a hob, which consists in rotating a blank, in 'cutting the blank to form a thread having involute heli-y coidal surfaces, in cutting straight flutes on the blank through the thread to formv teeth. having non-radially arranged cut-ting faces, in providing' a (formed cutting tool having a cutting edge shaped to the edge formed by the flutes on one of the involute helicoidal surfaces` in sol setting the cutting tool relative toy the blank teeth that the cutting edge of the tool matches `thefcntting edge on one side of each blank tooth, in feeding the tool alo-ng the blank in accorchulce With the pitch of the thread While effecting side relieving movements, and in'relievin the opfp-osite side ofl eac-h toothl in a similar manner. p

.23. The method of forming a hob, Which consists in rotating a blank, in cutting the 'blank to 'form a threadhaving involute "and in relieving the opposite side of' eachv blank through the thread to form teeth having non-radially arranged cutting faces, in providing a. formed. cutting tool having a cutting edge shaped to the edge formed by the fiutes on one of the involute helicoidal surfaces, in so setting the cutting tool relative to the blank teeth that the cutting edge of the tool matches the cutting edge on one side of each blank tooth, in feeding the tool along the blank in accordance with the pitch of the thread while effecting side relieving movements, in relieving the opposite side of each tooth in a similar manner, and in radially relieving the top edge of the teeth on the blank.

f 24. The method of forming a hob, which consists in rotating a blank, in cutting the blank to form a thread having helicoidal surfaces, in cutting straight fiutes on the blank through the threadto form teeth having non-radially arranged cutting faces, in

providing a formed cutting tool having the lit) cutting edge shaped to the edge formed by the fiutes of one -of the helicoidal surfaces, in so setting the cutting tool relative to the blank teeth that the cutting edge of the tool matches the cutting edge on one side of each blank tooth, in feeding the tool along the blank in accordance With the pitch of the thread While effecting side relieving movef ments, in relieving the opposite sideof each tooth in a similar manner, in radially relieving the top side of each of the teeth on the blank, and in grinding the front cutting faces and the side cutting edges of the teeth.

25. The method of forming a hob, which consists in rotating a blank, in cutting the blank to form a thread having involute helicoidal surfaces, in cutting straight flutes on the blank through the thread to form teeth having non-radially arranged cutting faces,'in providing a formed cutting; to0l having a cutting edge 4shaped to the edge formed by the flutes on one of the involute helicoidal surfaces, in so setting the cutting tool relative to the blankteeth that the cut ting edge off-the tool matches the cutting edge on one side of each blank tooth, in feeding the tool along the blank in accordance Withthe pitch of the thread Whilr` effecting side relieving movements, in relieving the opposite side of each tooth ina similar manner, in radially relieving the top edge of the teeth on the blank, and in grinding the front cutting faces and the side cutting edges of the teeth.

26. The method of forming a hob, \vhich consists in rotating a blank, in providing a cutting tool inengagement with the rotating blank, said cutting tool having one straight cutting edge tangent on one side of the blank axis to thebase-cylinder of a desired involute helicoid and making a predetermined angle with a plane perpendicular to the blank axis, in moving said cutting tool along the blank to form an involute helicoidal surface,in moving a cutting edge along the blank to form a second involute lhelicoidal surface having the same lead as the otherhelicoidal surface, said last cutting edge being tangent, on the side of the blank axis Vopposite to the first cutting position, to the base cylinder of the desired involute'helicoid and makes a predetermined angle with a plane perpendicular to the blank axis, in cutting flutes on the blank through vsaid -helicoidal surfaces to form teeth, and in relieving the teeth formedby said flutes.

i 27. rlhe method of forming a hob, which consistsin rotating a blank, in providing a cutting tool in engagement With the rotating blank, said cutting tool having one straight cutting edge tangent on one side of the blank axis to the base cylinder of, adesired involute helicoid and making a predetermined angle with a Aplane perpendicular to the blank axis,` in moving said cutting 'tool' along the blank to form an involute helicoidal surf-ace, in moving a cutting edge along the blank to form a second involute helicoidal surface having the 'same lead as the other helicoidal surface, said last cutting edge being tangent, on the side of the blank axis opposite to the first cutting position, to the base cylinder of the desired involute helicoid `and makes la predetermined anglewith a plane perpendicular to the blank axis, in 'cutting flutes on the blank through said helicoidal surfaces to form teeth, and in side relieving the cutting edges ofthe teeth formed by saidpfiutes so that the effective contour behind each cutting surface is the same at successive surfaces of intersection similar to the .initial cutting face whereby the blank'may be ground on the front cutting face 'without changing the effective contour.

28. The method of forming a hob, Whichconsists in rotating a blank, in providing a .cutting tool in engagement "with the rotat` ing lank, said cutting tool having one straight cutting edge tangent on one side' of the blank axis to the base cylinderofa desired involute helicoid and making a pre'- determined angle with a plane per end'icular to the blank axis, in moving sai cutting tool lalong the; blank te form an involute helicoidal surface, in moving a cutting edge along the blank to form a`. second involute4 helicoidal surface having the same lead as the other helicoidal surface, said last cutting edge being tangent, on the side of the blank axisopposite tothe first cuttingposition, to the base cylinder of the desired. involute helicoid and makes a predetermined angle With a plane perpendicular to the blank axis,

`iiadially relieving thetops of the'teeth.

in cutting flutes on rthe, blank through'said helicoldal surfaces to form teeth, in side relieving the sides of the teeth, and in ,25). The method of forming a hob, which consists in rotating a blank, in rotatingr a formed milling cutter, in engagement with the blank while eti'ectingaxial movement between the'cutter andthe blank to form a thread having app'proximate involute helicoidal surfaces, in setting acutting tool in engagement with' the rotating bla-nk, said tool having a cutting edge-tangent to the base cylinder of the ydesired involute vrhelicoid'. and making a predetermined angle with a plane perpendicular'to the blank' axis to cut an involute helicoidal surfaceon one side of the blank thread, in forming a similar involute helicoid on the opposite side of the lblank thread, in 'cuttingiiutes on the blank, and in sigle relieving the sides with a plane/perpendicular totheblank axis to cutan involute helicoidal surface on one side ofthe blank thread, in forming a similar involute helicoid on the opposite side of the blank thread, in side relieving the sides -of the teeth formed by saidflutes, and in grinding the front cutting faces and the side cutting edges of the-teeth.

` 3l. TheV method of forming a hob, ivhich consists in rotating ablank, in rotating a formed milling cutter. in engagement with the blank while effecting axial 'movement between the cutter and the blank to form. a thread having approximate' involute' helie coidal surfaces, in setting a cutting tool in engagement with the rotating blank, saidtool having a cutting edge tangent to the base cylinder of the'desired involute helicoid and making a predetermined angle With a plane perpendicularto theblank axis to cut an involute Surface on one side of the blank thread, in forming a similar involute helicoid` on the opposite4 side of the blank thread, in cutting flutes onA the blank, in side relieving the sides of the teeth formed by Vsaid flutes, and in radially-relieving the tops of tleteeth. 32. The method of forming a hob, which consists in rotating a blank, in rotating a formed milling cutter in engagement with the blank While eecting axial feeding, movement between the cutter and the blank volute helicoidal surfaces, in setting a cuttzng tool m engagement with the rotatmg Y blank to cut an involute helicoidal surface on one side of the blank thread, said too-l having a cutting edge tangent on one side of the-blank axis to the base cylinder of the desired involute helicoid and making a predeterminedvangle with a plane-perpendicular to-the blank axis, in cutting an involute surface on the other` side of the blank thread by setting a straight cutting edge in engagement with theretating blank, said cutting edge being tangent, on the side of the blank axis opposite to the first cutting position, to the cylinder of the desired involute helicoid land makes a predetermined angle withv a plane perpendicular to the blank axis for cutting an involute'helicoidal surface o-n the oppositeside of the blank thread, in cutting flutes on the blank, and in relieving the teeth formed by said liutes. 33. The method of forming a hob, which consists in rotating av blank,`in rotating a formed 4milling cutter in engagement With the blank While effecting axialfeedingfmove ment between thecutter and the blank to` form 'a thread having approximate involuteA helicoidal surfaces, in setting a cutting tool A in engagement with the rotating blank to cut an involute helicoidal surface on one side of the blank thread, said tool having' a cutting edge tangent o-n one 4side of the blank axis to the base cylinder of the desired involute helicoid and making apre-` 'determined angle with a planeperpendifcular to the blank axis, in cutting an involute surface on the other side of the blank thread by set-ting a straight cutting edge in engage-` ment with the .rotating blank, said cutting edge being tangent, on the side of the'blank axis opposite to the first cutting position,

to the cylinder 'of the desired involute heli-Y coid and makes a predetermined angle with a. plane perpendicular to the blank axis for fective contour behind each cutting surface is'the same at successive surfaces of intersectionf similar to the initialcutting face. 34. The method of forming a hob, which consists in rotating a blank, in forming a thread on the blank having involute helicoidal surfaces, in cutting flutes on the a constant relief on the involute helicoidal surfaces of the heb teeth while maintaining the-lead unchanged, whereby the effective- 35. v The method of forming a hob, which vvconsists lin rotating a blank, in forming a effective contour behind leach cutting surthread having involute helicoidal surfaces, face is the same at successive surfaces of in cutting flutes on the' blank-through the intersection similar to the initial cutting 10 thread to form teeth, in effecting constant face, relief on the sides of the teeth While main- In testimony whereof, I hereto ,aiiix my l taining the lead iinchanged, and in radially signature.

relieving the tops of the/teeth so that the. EARLE BUCKINGHAM. 

